The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. When the adaptive mesh refinement scheme is used, the fine mesh still remains along the path where crack already passed. However, structural properties such as stiffness, damage and strain energy of an element completely partitioned by the crack path remain almost unchanged during the rest of the simulation. Using the phantom-node method, the fine mesh in the crack path domain is recovered into a coarse mesh. This numerical scheme significantly reduces the number of degrees of freedom involved in the computation. Using the mesh coarsening method together with the adaptive mesh refinement and adaptive update schemes, the computational cost is further reduced. Through several numerical examples, the performance of the proposed method is demonstrated.

相场模型采用幻像节点法进行网格粗化，以提高计算效率。当使用自适应网格细化方案时，细网格仍然沿着裂纹已经通过的路径保留。然而，在其余的模拟过程中，被裂纹路径完全分割的单元的刚度、损伤和应变能等结构特性几乎保持不变。使用幻像节点方法，将裂纹路径域中的细网格恢复为粗网格。该数值方案显着减少了计算中涉及的自由度数量。将网格粗化方法与自适应网格细化和自适应更新方案结合使用，进一步降低了计算成本。通过几个数值例子，证明了所提出方法的性能。